A Nuclear Reaction: Determining the velocity of neutrons

In summary, the conversation discusses the process of fission in nuclear power plants, where a heavy nucleus splits into two medium-sized nuclei and releases energy. One example of this is when a neutron colliding with a 235U nucleus splits it into a 141Ba nucleus and a 92Kr nucleus, while also releasing two neutrons. The question posed is what are the speeds of the two neutrons after the collision, given the initial and final velocities of the incoming neutron. The solution involves using the conservation of momentum equations for the x and y directions. There was a rounding error in the original answer, and the correct final answers for the speeds of the two neutrons are 220 m/s and 1000 m/s.
  • #1
maxd23
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Homework Statement



Fission, the process that supplies energy in nuclear power plants, occurs when a heavy nucleus is split into two medium-sized nuclei. One such reaction occurs when a neutron colliding with a 235U (uranium) nucleus splits that nucleus into a 141Ba (barium) nucleus and a 92Kr (krypton) nucleus. In this reaction, two neutrons also are split off from the original 235U. Before the collision, the arrangement is as shown in the figure (a). After the collision, the 141Ba nucleus is moving in the +z - direction and the 92Kr nucleus in the −z - direction. The three neutrons are moving in the xy-plane, as shown in the figure (b) (Figure 1) .[/B]

If the incoming neutron has an initial velocity of magnitude 3.0×10^3m/s and a final velocity of magnitude 2.0×10^3m/s in the directions shown, what are the speeds of the other two neutrons? (The mass of the 141Ba nucleus is approximately 2.3×10^−25kg, and the mass of 92Kr is about 1.5×10^−25kg.)

Homework Equations



Pi_x=Pf_x

Pi_y=Pf_y

The Attempt at a Solution



I have tried this problem several different ways and keep getting stuck. I have been told my approach is correct, however there are some errors present. Can someone please help me through this problem. Thank you
IMG_0502.jpg

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  • #2
Hello. Welcome to PF.

Your work looks good to me. How do you know there are errors present? Your final answer for Vn1 has been rounded to only one significant figure.
 
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  • #3
TSny said:
Hello. Welcome to PF.

Your work looks good to me. How do you know there are errors present? Your final answer for Vn1 has been rounded to only one significant figure.
T

here was a rounding error, the final answer is 220 m/s and 1000 m/s

Thanks
 
  • #4
OK. Good work!
 
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What is a nuclear reaction and why is it important?

A nuclear reaction is a process in which the nucleus of an atom is altered, resulting in a change in the atom's identity and releasing a significant amount of energy. It is important because it is the basis for nuclear power, nuclear weapons, and many other applications such as medical treatments and scientific research.

How do scientists determine the velocity of neutrons in a nuclear reaction?

Scientists use a variety of techniques to determine the velocity of neutrons in a nuclear reaction. One common method is to measure the time it takes for the neutrons to travel a known distance, using specialized detectors to accurately measure their arrival time. Another method is to use a process called neutron moderation, in which neutrons are slowed down by passing through a material in order to measure their velocity.

What factors can affect the velocity of neutrons in a nuclear reaction?

The velocity of neutrons in a nuclear reaction can be affected by a number of factors, including the type of reaction taking place, the energy level of the particles involved, and the surrounding environment. Additionally, the presence of other particles or materials can also impact the velocity of neutrons.

Why is it important to accurately determine the velocity of neutrons in a nuclear reaction?

Accurately determining the velocity of neutrons in a nuclear reaction is crucial for understanding the behavior of the reaction and its potential outcomes. This information is essential for safety protocols and for optimizing the efficiency of nuclear processes. It also plays a crucial role in the development of new technologies and advancements in the field of nuclear science.

Can the velocity of neutrons in a nuclear reaction be controlled?

Yes, the velocity of neutrons in a nuclear reaction can be controlled. This is often achieved through the use of materials that can slow down or absorb neutrons, known as neutron moderators and neutron absorbers, respectively. By carefully controlling the velocity of neutrons, scientists can manipulate the behavior of a nuclear reaction and its resulting energy output.

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